Question

what is value of (1+3+5+7+....+4033)+7983×2017

Answer 1

First of all we solve the numbers in the small bracket and we get 4049 as answer while the other hand we will multiply the 7983 with 2017 and answer is 16101711.
And atlast, we will sum up the both answers and the result is 16105760.

Answer 2

Answer:

$(1+3+5+7+....+4033)+7983\times 2017=20170000$

Step-by-step explanation:

Given : Expression $(1+3+5+7+....+4033)+7983\times 2017$

To find : The value of the expression ?

Solution :

Expression $(1+3+5+7+....+4033)+7983\times 2017$

Taking, $1+3+5+7+....+4033$ forming an Arithmetic progression

with first term a=1 , common difference d=2 and last term l=4033.

First we find the number of terms,

$l=a+(n-1)d$

$4033=1+(n-1)2$

$\frac{4032}{2}=n-1$

$2016+1=n$

$n=2017$

The sum of the series is

$S_n=\frac{n}{2}[a+l]$

$S_n=\frac{2017}{2}[1+4033]$

$S_n=\frac{2017}{2}\times 4034$

$S_n=2017\times 2017$

$S_n= (2017)^2$

Substitute in the expression,

$=(2017)^2+7983\times 2017$

$=2017(2017+7983)$

$=2017(10000)$

$=20170000$

Therefore, $(1+3+5+7+....+4033)+7983\times 2017=20170000$